Piaget’s Theory (Concrete & Formal Operational Stages)

Piaget’s theory, in regards to cognitive development, states that as humans develop they go through four stages. Each stage corresponds with a different way of thinking and understanding the world. As individuals advance to the next stage, their thinking and understanding of the world becomes more abstract and complex. Each stage corresponds with a specific range of ages as well; however, the ages can vary depending on the developmental situation of the individual (1.2). The four stages are sensorimotor, pre-operational, concrete operational, and formal operational. The two more advance stages are the concrete and formal operational stages.

The concrete operational stage includes those who are approximately in-between ages 7 to 11 years old. During this stage children are able to reason logically as long as the reasoning can be applied to concrete and specific examples. In this stage they are also able to observe and understand the idea of conservation. For example, if a specific amount of water is poured into a tall, skinny glass and then poured into a short, wide glass, concrete operational thinkers are able to understand that the volume of the water did not change. Overall, logical reasoning is present in this stage, but cannot be utilized unless applied to concrete examples.

The formal operational stage follows the concrete operational stage. Those who are in this stage are roughly 11 to 15 years old and are advancing from logical reasoning with concrete examples to abstract examples. The need for concrete examples is no longer necessary because abstract thinking can be used instead. In this stage adolescents are also able to view themselves in the future and can picture the ideal life they would like to pursue. Some theorists believe the formal operational stage can be divided into two sub-categories: early formal operational and late formal operation thought. Early formal operational thoughts may be just fantasies, but as adolescents advance to late formal operational thought the life experiences they have encountered changes those fantasy thoughts to realistic thoughts (Broughton, 1983).

In conclusion, Piaget viewed adolescents as either in the concrete or formal operational stage. In each stage, adolescents think differently and as a result they learn differently (2.1). It is important for teachers, parents, and other influential people in adolescents’ lives to understand these different stages to be able to provide the appropriate learning tools. Without the appropriate learning tools, adolescents are unable to effectively learn and are unable to gain enough knowledge and experience to advance to the next developmental stage.



As a high school teacher it is important to know which developmental stage the students are in. Most high school students are either in the concrete or formal operational stage. In mathematics it is especially important to know how to teach certain concepts. Some students may be able to understand the concepts with an abstract explanation and some may need a concrete example.

One concept I may be teaching is adding, subtracting, multiplying, and dividing with negative numbers. Some students may be able to do these types of problems without a physical example. For those students who need a concrete example, I will use a number line to show how adding, subtracting, multiplying, and dividing with negative numbers works.